A Method for Constructing Self-orthogonal Codes Over Finite Fields
Zhang Fu-li① Kai Xiao-shan① Zhu Shi-xin① Chen An-shun②
①(School of Mathematics, Hefei University of Technology, Hefei 230009, China) ②(School of Mathematical Sciences, Chuzhou University, Chuzhou 239000, China)
Abstract:A method is proposed to construct self-orthogonal codes over the finite field by Fq using cyclic self- orthogonal codes over the finite ring Fq+uFq. A Gray map from Fq+uFq to Fpq is introduced, and a sufficient and necessary condition for the existence of cyclic self-orthogonal codes over is given. It is proved that the Gray image of a cyclic self-orthogonal code with length n over Fq+uFq is a self-orthogonal code with length pn over Fq. Further, some self-orthogonal codes over Fq with good parameters are constructed.